Microelectromechanical sensor (MEMS) devices, such as mechanical resonators and inertial sensors, utilize mechanical suspensions to tailor their response to drive inputs and inertial forces along specific axes. These suspensions are designed to provide optimal sensitivity to desired input while at the same time minimizing sensitivity to undesired input. An area of particular importance is minimizing rotational motion of a sensor's proof masses in response to substantially linear input forces. Rotational motion of a proof mass contributes to inaccurate sensor output, reduced sensitivity to linear input forces, and an overall decrease in a number of other meaningful performance characteristics.
An example MEMS device with suspension elements, whose resistance to rotational motion is particularly critical, is an out-of-plane tuning fork gyroscope (OPG). An OPG typically includes at least two proof masses with an upper substrate disposed above each proof mass and/or a lower substrate disposed below each proof mass.
Further, an OPG typically has lateral drive motors (e.g., comb drive motors) on either side of the proof masses, driving the proof masses to continuously vibrate along a lateral drive axis at a motor resonant frequency, similar to the halteres of insects. With a rotational input about an axis perpendicular to the plane of the substrates, the proof masses experience Coriolis forces perpendicular to the drive axis and perpendicular to the input rotation axis. The Coriolis forces produce equal and opposite motion (differential displacement) of the two proof masses parallel to the plane of the substrates and perpendicular to the drive axis. This differential displacement of the proof masses is measured by transducers, which typically consist of interdigitated comb finger pairs, one member of each pair being attached to the substrates, the other member being attached to a proof mass, in order to form a sense capacitance. In the presence of a DC sense bias voltage on the sense capacitance, differential displacement of the proof masses results in a change in the charge on the sense capacitance proportional to the input rotation rate. Typically, the change in charge is converted to an output voltage by an electronic amplifier. The ratio of the output voltage to the input rotation rate defines the scale factor of the device.
FIG. 1 illustrates a prior art OPG 10 having multiple suspended proof masses 20 coupled to a crossbar portion 12 with multiple flexure suspension elements 16 of uniform stiffness. Drive motion of the OPG 10 is coupled between the proof masses 20 with anchored suspension elements 18 that lie along a sense axis 32 in plane with and between the proof masses 20. The arrows 22 and 26 running parallel with the sense axis 32 represent a direction of an on-axis response, whereas the arrows 24 and 28 running perpendicular to the sense axis 32 represents a direction of an off-axis response. In this configuration, a sense axis motion, represented by arrows 22 and 26, runs parallel with the sense axis 32, whereas a drive axis motion, represented by arrows 24 and 28, runs perpendicular with the sense axis 32; both motions are in plane with the OPG 10. An undesirable rotational motion of the proof masses occurs about an axis 30 perpendicular to the plane of the OPG 10.
FIG. 2-1 illustrates a diagram showing the suspension element 18 experiencing a differential force (arrows 50 and 52). FIG. 2-2 illustrates a diagram showing the anchored suspension element 18 experiencing a common mode force (arrows 46 and 48). The differential force produces a significant bend in the suspension element 18 (a low-stiffness response) having stressed right and left side portions. The opposing differential input forces can cause an undesired rotation of the proof masses 20 about the axis 30. The common mode force does not cause the suspension element 18 to bow (a high-stiffness response) in response to a uniform common mode input force.
Further, the motion of the combined flexure suspension elements 16 and the anchored suspension elements 18 along the drive axis 28 can interfere with a desired differential motion of the proof masses 20 along the sense axis 26. This interference causes a differential sense motion to have an adverse rotational character (see FIG. 3), as opposed to a desired purely translational character. Other important performance characteristics are also negatively impacted, including a reduced electrostatic spring softening of a sense mode, a reduced electrostatic actuator strength of associated force rebalance torquer electrodes, and a reduced sensitivity of a sensor to desired rotational input (measured as a scale factor).